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Identification of frequency of a shifted sinusoidal signal. (English. Russian original) Zbl 1155.93026
Autom. Remote Control 69, No. 9, 1447-1453 (2008); translation from Avtom. Telemekh. 2008, No. 9, 3-9 (2008).
Summary: The article deals with the issue of identification of an unknown frequency of a shifted sinusoidal signal \(y(t) = \sigma _{0} + \sigma sin(\omega t + \varphi )\). A new approach taken to estimate the frequency of a shifted sinusoidal signal is suggested, which is a robust approach relative to undetermined disturbances present in the measurement of a useful signal. In contrast to known analogs, the given approach permits controlling the time of estimation of the unknown frequency \(\omega \). The dimension of the identification algorithm suggested is less than that of known analogs.

93C15 Control/observation systems governed by ordinary differential equations
93B30 System identification
Full Text: DOI
[1] Clarke, D.W., On the Design of Adaptive Notch Filters, Int. J. Adapt. Control, 2001, vol. 15, pp. 715–744. · Zbl 1056.93061 · doi:10.1002/acs.652
[2] Wonham, W.M., Linear Multivariable Control: A Geometric Approach, New York: Springer-Verlag, 1979. Translanted under the title Lineinye mnogomernye sistemy: geometricheskii podkhod Moscow: Nauka, 1980.
[3] Nikiforov, V.O., Gutner, I.E., and Sergachev, I.V., The System of Active Vibroprotection: Development, Results of Tests, and Perspectives of Development, Mekhatron. Avtomatiz. Upravlen., 2004, no. 2, pp. 13–22.
[4] Lyamin, A.V., Shiegin, V.V., and Bobtsov, A.A., Path-Following and Adaptation of Wheeled Mobile Robots for Motion Along Unknown Paths, 29 Int. Sympos. Robot., Birmingham, 1998, pp. 211–214.
[5] Bobtsov, A.A., Dudarenko, N.A., and Lyamin, A.V., Trajectory Control of a Two-Drive Robot Using Methods of Adaptation and Self-Learning, Mater. nauch. shk.-konf. ”Mobil’nye roboty i sistemy,” (Mater. Scient. Sch.-Conf. ”Mobile Robots and Systems”), Moscow: Mosk. Gos. Univ., 2000, pp. 114–126.
[6] Bodson, M. and Douglas, S.C., Adaptive Algorithms for the Rejection of Periodic Disturbances with Unknown Frequencies, Automatica, 1997, vol. 33, pp. 2213–2221. · Zbl 0900.93146 · doi:10.1016/S0005-1098(97)00149-0
[7] Hsu, L., Ortega, R., and Damm, G., A Globally Convergent Frequency Estimator, IEEE Trans. Automat. Control, 1999, vol. 46, pp. 967–972. · Zbl 0958.93089
[8] Mojiri, M. and Bakhshai, A.R., An Adaptive Notch Filter for Frequency Estimation of a Periodic Signal, IEEE Trans. Automat. Control, 2004, vol. 49, pp. 314–318. · Zbl 1365.94084 · doi:10.1109/TAC.2003.821414
[9] Marino, R. and Tomei, R., Global Estimation of Unknown Frequencies, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 1324–1328. · Zbl 1364.93778 · doi:10.1109/TAC.2002.800761
[10] Xia, X., Global Frequency Estimation Using Adaptive Identifiers, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 1188–1193. · Zbl 1364.93789 · doi:10.1109/TAC.2002.800670
[11] Obreg’on-Pulido, G., Castillo-Toledo, B., and Loukianov, A.A., Globally Convergent Estimator for n-Frequencies, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 857–863. · Zbl 1364.62222 · doi:10.1109/TAC.2002.1000286
[12] Bobtsov, A., Lyamin, A., and Romasheva, D., Algorithm of Parameter’s Identification of Polyharmonic Function, 15 IFAC World Congress Automat. Control, Barcelona, 2002.
[13] Bobtsov, A.A. and Kremlev, A.S., Adaptive Identification of Frequency of a Shifted Sinusoidal Signal, Izv. Vuzov, Priborostr., 2005, no. 4, pp. 22–26.
[14] Hou, M., Amplitude and Frequency Estimator of a Sinusoid, IEEE Trans. Automat. Control, 2005, vol. 50, pp. 855–858. · Zbl 1365.93485 · doi:10.1109/TAC.2005.849244
[15] D’yakonov, V., MATLAB6. Uchebnyi kurs (MATLAB 6. Course of Studies), St. Petersburg: Piter, 2001.
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